Year: 2021
Author: Liangya Pi, Yong Yu, Yangwen Zhang, Gang Chen, Liangya Pi, Yangwen Zhang
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 144–175
Abstract
A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions, body forces, and time depending coefficients is developed. For ensemble solutions in $L^∞$($0$, $T$; $L^2$($Ω$)), a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree $k$ ≥ $0$ is established. The results of numerical experiments are consistent with the theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0190
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 144–175
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: HDG method ensemble methods parameterized convection diffusion PDEs numerical analysis.